Class 12th

Directions: Answer the questions based on the following Graph.

The line graph given below shows the marked price, selling price and cost of manufacturing of an aircraft  (in crore).

In which year, company records the highest profit on an aircraft?

A plane P contains the line x + 2y + 3z + 1 = 0 x – y – z – 6, and is perpendicular to the plane -2x + y + z + 8 = 0. Then which of the following points lies on P?

Let $\theta \in \left(0,\frac{\pi }{2}\right).$ $\frac{}{}$ If the system of linear equations.

$\left(1+co{s}^2\theta \right)x+si{n}^2\theta y+4sin3\theta z=0$

$co{s}^2\theta x+\left(1+si{n}^2\theta \right)y+4sin3\theta z=0$

$co{s}^2\theta x+si{n}^2\theta y+\left(1+4sin3\theta \right)z=0$

has a non trivial solution, then the value of is:

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set:

Directions for questions: Answer the following questions based on the information given below.

The above graph shows the number of cars owners of three different company in eight different states of India.

If SUZUKI, FORD and TATA have each decided to facilitate service centre in those cities where its cars owners are highest in number, which of the following cities will avail themselves of this facility?

The number of bridged oxygen atoms present in compound B formed form the following reaction is   $Pb{\left(N{O}_3\right)}_2\stackrel{673K}{\to }A+PbO+O_2$ ${{}_{}}_{}\stackrel{}{}{}_{}$

$A\stackrel{Dimerise}{\to }B$

Directions for questions: Answer the following questions based on the information given below.

The above graph shows the number of cars owners of three different company in eight different states of India.

By what percent the number of TATA cars owner in Surat is less than that of Suzuki in Darjeeling ?

Let a,b $\in R,b\ne 0.$  Define a function f(x) =   $\{\begin{array}{cc}\hfill asin\frac{\pi }{2}\left(x-1\right),\hfill & \hfill forx\le 0\hfill \\ \hfill \frac{tan2x-sin2x}{b{x}^3},\hfill & \hfill forx>0\hfill \end{array}$

If f is continuous at x = 0, then 10 – ab is equal to__________

Let $z=\frac{1-i\sqrt[]{3}}{2},i=\sqrt[]{-1}.$  Then the value of

$21+{\left(z+\frac{1}{z}\right)}^3+{\left(z^2+\frac{1}{z^2}\right)}^3+{\left(z^3+\frac{1}{z^3}\right)}^3+.....+{\left(z^{21}+\frac{1}{z^{21}}\right)}^{3}is\_\_\_\_\_\_\_\_\_.$

Directions for questions: Answer the following questions based on the information given below.

The above graph shows the number of cars owners of three different company in eight different states of India.

In how many cities in India were there more than 13% of the total TATA cars owners in the country? Assume no other city besides the given eight cities has TATA cars owners.